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Locally Finite Root Systems

Ottmar Loos University of Innsbruck, Innsbruck, Austria
Erhard Neher University of Ottawa, Ottawa, ON, Canada
Available Formats:
Electronic ISBN: 978-1-4704-0412-3
Product Code: MEMO/171/811.E
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $36.00 Click above image for expanded view Locally Finite Root Systems Ottmar Loos University of Innsbruck, Innsbruck, Austria Erhard Neher University of Ottawa, Ottawa, ON, Canada Available Formats:  Electronic ISBN: 978-1-4704-0412-3 Product Code: MEMO/171/811.E  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$36.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1712004; 214 pp
MSC: Primary 17; 20;

We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: The intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.

Graduate students and research mathematicians interested in infinite-dimensional Lie theory.

• Chapters
• Introduction
• 1. The category of sets in vector spaces
• 2. Finiteness conditions and bases
• 3. Locally finite root systems
• 4. Invariant inner products and the coroot system
• 5. Weyl groups
• 6. Integral bases, root bases and Dynkin diagrams
• 7. Weights and coweights
• 8. Classification
• 9. More on Weyl groups and automorphism groups
• 10. Parabolic subsets and positive systems for symmetric sets in vector spaces
• 11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group
• 12. Closed and full subsystems of finite and infinite classical root systems
• 13. Parabolic subsets of root systems: classification
• 14. Positive systems in root systems
• 15. Positive linear forms and facets
• 16. Dominant and fundamental weights
• 17. Gradings of root systems
• 18. Elementary relations and graphs in 3-graded root systems
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 1712004; 214 pp
MSC: Primary 17; 20;

We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: The intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.

Graduate students and research mathematicians interested in infinite-dimensional Lie theory.

• Chapters
• Introduction
• 1. The category of sets in vector spaces
• 2. Finiteness conditions and bases
• 3. Locally finite root systems
• 4. Invariant inner products and the coroot system
• 5. Weyl groups
• 6. Integral bases, root bases and Dynkin diagrams
• 7. Weights and coweights
• 8. Classification
• 9. More on Weyl groups and automorphism groups
• 10. Parabolic subsets and positive systems for symmetric sets in vector spaces
• 11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group
• 12. Closed and full subsystems of finite and infinite classical root systems
• 13. Parabolic subsets of root systems: classification
• 14. Positive systems in root systems
• 15. Positive linear forms and facets
• 16. Dominant and fundamental weights
• 17. Gradings of root systems
• 18. Elementary relations and graphs in 3-graded root systems
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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